This week President George Bush is expected to address his nation. A speech he made last month to US servicemen and their families at a California airbase is a guide to what he is likely to say. Then, he told his audience at USAF Miramar that 'the terrorists are meeting the fate they chose' when they attacked America. The US was 'waging an unrelenting campaign against the global terror network - and we are winning.'

The President made three points to support his claim of incipient victory. The first is the success of counter-terrorist measures which have, he claimed, eliminated 'two- thirds of known al-Qaeda leaders and key operatives'. The second and third, American 'successes' in Afghanistan and Iraq.

Bush's claim that security authorities have ended the activities of a high proportion of those senior Islamic militants who were close to Osama bin Laden is, with certain glaring exceptions, true. Key members of the 11 September plot have been located and killed or captured.

Khaled Sheikh Mohammed and Abu Zubaydah, senior aides of bin Laden, have been apprehended along with hundreds of others.

Though many of the more junior militants picked up have little connection to bin Laden's group on the whole, the targets of US operations are dangerous men whose incarceration or death is critical in disrupting extant terrorist groups and preventing further attacks. This has been a considerable achievement.

There are other gains in the war on terror. Increased counter-terrorist budgets have made the movement of arms far harder, as was shown by the arrest in August, after a complex and expensive 'sting' operation, of a British national in America on charges of conspiring to import surface-to-air missiles.

Now even states that have previously dragged their feet are realising they have little choice but to co-operate with Washington. In Saudi Arabia, the country that has greatest responsibility for the creation of modern Islamic militancy, police have arrested more than 200 suspects since the bomb attacks in Riyadh in May. Elsewhere, states are co-operating with each other in an unprecedented way.

Australia, Thailand, Malaysia and Indonesia all claim a role in the capture near Bangkok last month of Riduan Isamuddin, aka Hambali, a key South-East Asian militant. Such co-ordination would have been unthinkable two years ago.

So if its aims are defined in strictly military terms - the termination of the activities of a group of enemy individuals - then the war on terror is going well. In which case why the practice operation for dealing with a dirty bomb in the City of London tomorrow? Why is British Airways considering fitting its planes with anti-missile equipment?

Why does Sir John Stevens, Britain's most senior policeman, think, like the Prime Minister, that a serious terrorist attack in Britain is 'inevitable'? Why does no one feel much safer than they did in the days after 11 September?

BUSH TOLD the California servicemen that Afghanistan is now 'a friend of the United States'. This is nonsense. There is a small elite in Kabul better disposed towards the US than might usually be expected of Afghans, but most of the residual goodwill felt by the general population has long since evaporated.

It was rooted in a hope that things might get better relatively rapidly. For most Afghans things have not improved much. The consequences are obvious. In the past two weeks fierce battles have been raging in south-eastern Afghanistan with a resurgent, reconstituted Taliban-like faction.

But the real concern must be Iraq. The problem here is not the Iraqis, who largely have yet to turn against the Americans, but in what the occupation, and the violence associated with it, is doing in the rest of the Islamic world. This is what Bush appears to be unable to comprehend. There is evidence that hundreds of Muslim militants have entered Iraq to join in a holy war against the Americans. The fact that the Iraqis welcomed the US and UK forces is not important to these fanatical volunteers. They believe that, since the Crusades, the West has been committed to the humiliation and subordination of Islam. They see their war as defensive. The American-led anti-terrorist operations have done nothing except confirm them in their world view.

Few new militants, however, can be linked to al-Qaeda. They are not on the list of individuals that Bush put in his desk drawer after 11 September. They are young Muslim men for whom the message of bin Laden and the movement of radical thought he represents make sense.

There is a temptation to try to make order out of the sheer variety and seeming incomprehensibility of contemporary terrorism. An easy way to do it is to lump it all together as the work of 'al-Qaeda'. If al-Qaeda means the group of men gathered by bin Laden in Afghanistan between 1996 and 2001, and responsible for 11 September, then al-Qaeda is finished. Its bases are destroyed, its personnel are scattered. If al-Qaeda is defined as the totality of modern Wahhabi- influenced Sunni Muslim militancy and its ideology, then al-Qaeda is very much alive.

The truth is that those who were responsible for the background of violence in South-West Asia, for the bombs in Bali, Mombasa, Casablanca and Riyadh, all belong to the extremist fringe of a movement with deep roots in the Islamic world.

This movement is so diverse that to reduce it to a label is wrong. It has its roots in the same factors that have made a substantial portion of the world, from the Maghreb to the Indonesian archipelago, an 'arc of instability'.

The 'al-Qaeda' mindset is a mix of revolutionary politics and ultra-conservative, millenarian religion. The primary purpose of the terrorist strikes is not to inflict damage on the West, or to achieve short-term political gains. It is to mobilise those Muslims who have hitherto rejected the extremists' violent message. The attacks are demon strations of faith, power and strength designed to convince and to motivate.

For men such as bin Laden and his key aide, Ayman al-Zawahiri, it is imperative that the masses heed their call. For only then, they believe, will a just and perfect society be created. No one need lack healthcare, satisfactory employment, adequate housing or, crucially, pride again.

This weekend Pakistani military helicopters, thought to be carrying US special forces troops, have been seen on the Pakistan-Afghan border where bin Laden is supposed to be hiding.

In December 2001, weeks after escaping the American bombing at Tora Bora, bin Laden said: 'If Osama lives or dies does not matter_ the awakening has started.' Anyone seeking to comprehend the extent of modern Islamic militancy would do well to bear in mind these words. Tragically, it seems he was right. An evil awakening has started. Are we winning the war on terror? Not yet.

· Jason Burke's Al-Qaeda: Casting a Shadow of Terror is published by I.B.Tauris